Question

Find the value of log tan 1degree +log tan 2 degree +log tan 3 degree

Answer 1

Hello Dear Brainly user...

According to me

Question is:-

Find the value [ log tan1° + log tan2° + log tan3° .......+ log tan88° + log tan89° ] = ?

Solution:-

we know that:-

(i) log m + log n = log m×n

(ii) tan x = cot (90° - x)

(iii) tanx × cotx = 1

(iv) log 1 = 0

Here:-

= [ log tan1° + log tan2° + log tan3° .......+ log tan88° + log tan89° ]

= [ log ( tan1° × tan2° × tan 3° ..× tan 45° ... × tan 87° × tan 88° × tan 89°) ]

= [ log ( tan1° × tan2° × tan 3° ..× tan 45° ... × cot(90°- 87°) × cot(90°- 88°) × tan(90°- 89°) ]

= [ log (tan1° × tan2° × tan 3° ..× tan 45° ... × cot 3° × cot 2° × cot 1°) ]

= log 1 = 0 answer

Hope it helps.. :-)